Question: Rewrite as a simplified fraction. ${0.1\overline{29} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 129.2929...\\ 10x &= 1.2929...\end{align*}}$ Subtracting the two equations, we have: ${990x = 128}$ ${x = \dfrac{128}{990}} $ ${x = \dfrac{64}{495}} $